ABC is a triangle with B as right angle, AC=5 cm and AB = 4 cm. A circle is drawn with A as centre and AC as radius. The length of the chord of this circle passing through C and B is
A. 3 cm
B. 4 cm
C. 5 cm
D. 6 cm
Answers
Given : ABC is a triangle with B as right angle, AC = 5 cm and AB = 4 cm. A circle is drawn with A as centre and AC as radius.
To find : The length of the chord of this circle passing through C and B .
Solution :
Let DC is a chord passing through B and C.
In ∆ABC, by using Pythagoras theorem :
AC² = AB² + BC²
5² = 4² + BC²
25 = 16 + BC²
BC² = 25 - 16
BC² = 9
BC = √9
BC = 3 cm
Since the perpendicular from the centre of a circle to a chord bisects the chord.
∴ CD = 2 BC
CD = 2 × 3
CD = 6 cm
Hence the length of the chord of this circle passing through C and B is 6 cm .
Among the given options option (D) 6 cm is correct.
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Answer:
Step-by-step explanation:
In ∆ABC, by using Pythagoras theorem :
AC² = AB² + BC²
5² = 4² + BC²
25 = 16 + BC²
BC² = 25 - 16
BC² = 9
BC = √9
BC = 3 cm
Since the perpendicular from the centre of a circle to a chord bisects the chord.
∴ CD = 2 BC
CD = 2 × 3
CD = 6 cm